Oh dear! What a pickle. I am glad you got out of an abusive relationship, but as your relationship with your husband is no longer subsisting your visa may be curtailed at any time, particularly if he informs the UKVI. Really, you should get on a visa that is applicable to your situation now, not based on a relationship that no longer exists (even if the marriage still does).
This might sound awful, but if the abuse is documented, there may be recourse to pursue a visa based on this abuse. Or you could look at getting a student visa or your work might be able to sponsor you. Or get divorced quickly and marry this new fella.
As far as moving to the US, my understanding is that you would either need to be married or prove intent to marriage. Otherwise your new boyfriend will have to independently move to America, either on a work or student visa in his own right. Just like for the UK, the US doesn't really have a 'shacking up visa' as we say here on the forum.
Most people on this site have moved TO the UK, but I reckon a few people might be along who have more info on moving to the US on a fiance/spouse route.